Statistics Papers

Document Type

Conference Paper

Date of this Version

2011

Publication Source

Advances in Neural Information Processing Systems

Volume

24

Abstract

Learning theory has largely focused on two main learning scenarios: the classical statistical setting where instances are drawn i.i.d. from a fixed distribution, and the adversarial scenario whereby at every time step the worst instance is revealed to the player. It can be argued that in the real world neither of these assumptions is reasonable. We define the minimax value of a game where the adversary is restricted in his moves, capturing stochastic and non-stochastic assumptions on data. Building on the sequential symmetrization approach, we define a notion of distribution-dependent Rademacher complexity for the spectrum of problems ranging from i.i.d. to worst-case. The bounds let us immediately deduce variation-type bounds. We study a smoothed online learning scenario and show that exponentially small amount of noise can make function classes with infinite Littlestone dimension learnable.

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Date Posted: 27 November 2017